A spring balance has a scale that reads from 0 to 50 kg.The length of the scale is 20 cm.A block of mass m is suspended from this balance,when displaced and released,it oscillates with a period 0.5 s. What is the value of m?[ g = 10 m s − 2 ]

Question

A spring balance has a scale that reads from 0 to 50 kg.The length of the scale is 20 cm.A block of mass m is suspended from this balance,when displaced and released,it oscillates with a period 0.5 s. What is the value of m?[  g  =  10  m      s          −      2      ]

Monica Dennis · Accepted Answer

I am guessing that the wording of the question means that the spring stretches from 0 to 20 cm as the weight increases from 0N to 500 N. This means that the spring constant is  k  =            500      N              0.2      m        =  2500  N      m          −      1      The time period of oscillations of a mass m attached to a spring with spring constant k is given by  T  =  2  π            m      k      Thus  m  =  k  (      T          2      π            )          2        ≈  2500  N      m          −      1        (            0.5      s              2      ×      3.14            )          2        =  15.8  K  g